What is the Greatest Common Factor of 36100 and 36114?

Greatest common factor (GCF) of 36100 and 36114 is 2.

GCF(36100,36114) = 2

We will now calculate the prime factors of 36100 and 36114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 36100 and 36114.

How to find the GCF of 36100 and 36114?

We will first find the prime factorization of 36100 and 36114. After we will calculate the factors of 36100 and 36114 and find the biggest common factor number .

Step-1: Prime Factorization of 36100

Prime factors of 36100 are 2, 5, 19. Prime factorization of 36100 in exponential form is:

36100 = 2² × 5² × 19²

Step-2: Prime Factorization of 36114

Prime factors of 36114 are 2, 3, 13, 463. Prime factorization of 36114 in exponential form is:

36114 = 2¹ × 3¹ × 13¹ × 463¹

Step-3: Factors of 36100

List of positive integer factors of 36100 that divides 36100 without a remainder.

1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 190, 361, 380, 475, 722, 950, 1444, 1805, 1900, 3610, 7220, 9025, 18050

Step-4: Factors of 36114

List of positive integer factors of 36114 that divides 36100 without a remainder.

1, 2, 3, 6, 13, 26, 39, 78, 463, 926, 1389, 2778, 6019, 12038, 18057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 36100 and 36114. The biggest common factor number is the GCF number.
So the greatest common factor 36100 and 36114 is 2.

Also check out the Least Common Multiple of 36100 and 36114